phd in mathematics education in uk

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PhD Pure Mathematics / Overview

Year of entry: 2024

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The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree in a discipline directly relevant to the PhD (or international equivalent) OR any upper-second class (2:1) honours degree and a Master’s degree at merit in a discipline directly relevant to the PhD (or international equivalent).

Other combinations of qualifications and research or work experience may also be considered. Please contact the admissions team to check.

Full entry requirements

Apply online

In your application you’ll need to include:

• The name of this programme
• Your research project title (i.e. the advertised project name or proposed project name) or area of research
• Your proposed supervisor’s name
• If you already have funding or you wish to be considered for any of the available funding
• A supporting statement (see 'Advice to Applicants for what to include)
• Details of your previous university level study
• Names and contact details of your two referees.

Programme options

Programme description

The The Department of Mathematics has an outstanding research reputation. The research facilities include one of the finest libraries in the country, the John Rylands University Library. This library has recently made a very large commitment of resources to providing comprehensive online facilities for the free use of the University's research community. Postgraduate students in the Department benefit from direct access to all the Library electronic resources from their offices.

Many research seminars are held in the Department on a weekly basis and allow staff and research students to stay in touch with the latest developments in their fields. The Department is one of the lead partners in the MAGIC project and research students can attend any of the postgraduate courses offered by the MAGIC consortium.

For entry in the academic year beginning September 2024, the tuition fees are as follows:

• PhD (full-time) UK students (per annum): Band A £4,786; Band B £7,000; Band C £10,000; Band D £14,500; Band E £24,500 International, including EU, students (per annum): Band A £28,000; Band B £30,000; Band C £35,500; Band D £43,000; Band E £57,000
• PhD (part-time) UK students (per annum): Band A £2393; Band B £3,500; Band C £5,000; Band D £7,250; Band E 12,250 International, including EU, students (per annum): Band A £14,000; Band B £15,000; Band C £17,750; Band D £21,500; Band E £28,500

Further information for EU students can be found on our dedicated EU page.

The programme fee will vary depending on the cost of running the project. Fees quoted are fully inclusive and, therefore, you will not be required to pay any additional bench fees or administration costs.

All fees for entry will be subject to yearly review and incremental rises per annum are also likely over the duration of the course for Home students (fees are typically fixed for International students, for the course duration at the year of entry). For general fees information please visit the postgraduate fees page .

Always contact the Admissions team if you are unsure which fees apply to your project.

Scholarships/sponsorships

There are a range of scholarships, studentships and awards at university, faculty and department level to support both UK and overseas postgraduate researchers.

To be considered for many of our scholarships, you’ll need to be nominated by your proposed supervisor. Therefore, we’d highly recommend you discuss potential sources of funding with your supervisor first, so they can advise on your suitability and make sure you meet nomination deadlines.

For more information about our scholarships, visit our funding page or use our funding database to search for scholarships, studentships and awards you may be eligible for.

Contact details

Our internationally-renowned expertise across the School of Natural Sciences informs research led teaching with strong collaboration across disciplines, unlocking new and exciting fields and translating science into reality.  Our multidisciplinary learning and research activities advance the boundaries of science for the wider benefit of society, inspiring students to promote positive change through educating future leaders in the true fundamentals of science. Find out more about Science and Engineering at Manchester .

Programmes in related subject areas

Use the links below to view lists of programmes in related subject areas.

• Mathematics

Regulated by the Office for Students

The University of Manchester is regulated by the Office for Students (OfS). The OfS aims to help students succeed in Higher Education by ensuring they receive excellent information and guidance, get high quality education that prepares them for the future and by protecting their interests. More information can be found at the OfS website .

You can find regulations and policies relating to student life at The University of Manchester, including our Degree Regulations and Complaints Procedure, on our regulations website .

Mathematics MPhil/PhD

London, Bloomsbury

The department is home to many internationally renowned mathematicians. Our students go on to pursue successful careers in a variety of settings, primarily as postdoctoral researchers or in the world of finance. Excellent networking opportunities are provided by our central London location and close research links to other London universities.

UK tuition fees (2024/25)

Overseas tuition fees (2024/25), programme starts, applications accepted.

• Entry requirements

A minimum of an upper second-class UK Bachelor’s degree in a relevant discipline or an overseas qualification of an equivalent standard. Where possible, candidates are always interviewed. For overseas candidates there will be an alternative interview by telephone or Skype.

The English language level for this programme is: Level 1

UCL Pre-Master's and Pre-sessional English courses are for international students who are aiming to study for a postgraduate degree at UCL. The courses will develop your academic English and academic skills required to succeed at postgraduate level.

Further information can be found on our English language requirements page.

If you are intending to apply for a time-limited visa to complete your UCL studies (e.g., Student visa, Skilled worker visa, PBS dependant visa etc.) you may be required to obtain ATAS clearance . This will be confirmed to you if you obtain an offer of a place. Please note that ATAS processing times can take up to six months, so we recommend you consider these timelines when submitting your application to UCL.

Equivalent qualifications

Country-specific information, including details of when UCL representatives are visiting your part of the world, can be obtained from the International Students website .

International applicants can find out the equivalent qualification for their country by selecting from the list below. Please note that the equivalency will correspond to the broad UK degree classification stated on this page (e.g. upper second-class). Where a specific overall percentage is required in the UK qualification, the international equivalency will be higher than that stated below. Please contact Graduate Admissions should you require further advice.

About this degree

We offer research supervision across a broad range of pure and applied mathematics. General areas of expertise in pure mathematics include analysis, geometry, number theory and topology. In applied mathematics key areas of activity include fluid dynamics, mathematical modelling, mathematical physics, mathematical biology, applied and numerical analysis and financial mathematics.

Who this course is for

Our research degree programme is aimed at graduate students in mathematics or related sciences. Applicants will have analytical skills, and have formed a strong interest in pursuing mathematical research.

What this course will give you

The department offers a unique combination of outstanding research supervision and a rich community of students. It is sufficiently large for wide-ranging research activity but remains compact enough for academic staff to be highly accessible.

UCL’s role in the London School of Geometry and Number Theory (LSGNT) and London Taught Course Centre, as well as numerous intercollegiate seminars, ensures that students are firmly integrated into the wider mathematical community.

Some PhD projects are supervised jointly with industrial partners, or with other UCL departments or by interdisciplinary centres, with a unique critical mass of interdisciplinary activities at UCL.

The foundation of your career

Many of our students have go on to careers in financial services in the City; others have proceeded to postdoctoral research and academic careers.

Employability

Recent graduates have taken up academic posts at universities such as UCL, Imperial College London, Michigan, Sheffield, Mexico, Kyoto, California State, Others have joined the financial services industry with companies such as Barclays Capital, Schroders, Deloitte, ABN Amro and J. P. Morgan; Other graduates have become mathematics teachers and computer programmers.

A further example of employer destinations in industry would be Formula One motor racing development. Some students have summer secondments, such as two recent summer secondments at the Department of Business, Innovation and Skills.

Students closely interact with their peers from other London universities via the London Taught Course Centre, which offers a programme of advanced courses in mathematics and statistics one day a week for PhD research students in the region, as well as short intensive courses open to students from elsewhere in the UK and Europe.

You will have the chance to attend the departmental postgraduate seminar run by the students for the students, as well as other seminars both within and outside the department. You'll also have the opportunity to take part in a vigorous conferences programme.

Conferences recently hosted by the department include the Numerical Methods for MFG and related PDE Workshop, a lecture course on Regularity of Area Minimising Hypersurfaces, a conference on contact geometry and the British Applied Mathematics Colloquium, and the London Mathematical Biology Conference.

Teaching and learning

The degree is predominantly research-based and is overseen by a Principal Supervisor. Additionally all students are required to undergo training aimed at developing their presentation skills and gaining a broader knowledge of mathematics through modules (e.g. those offered by the London Taught Course Centre), seminars and conference attendance.

After 12-18 months, students are upgraded from MPhil to PhD candidature subject to assessment by a panel on the basis of a written report and oral examination. Ultimately, the student submits a thesis meeting the requirements of a UCL research degree as assessed by nominated examiners at an oral examination.

In a typical week you will meet your supervisory team for up to 2 hours. Short lecture courses, attending seminars, conferences or group meetings will amount to several additional hours per week. The majority of time is self-directed study.

Research areas and structure

Departmental research specialities fall within the two main groupings of pure and applied mathematics described below, and graduate research may be pursued within either field.

• Applied mathematics : environmental flows (including vortex dynamics, atmospheric and ocean dynamics and climate modelling); fluid mechanics (e.g. free-surface flows, polymers); industrial mathematics (e.g. inverse models, sound transmission, multi-particle interactions); mathematical biology and medicine (e.g. modelling cerebral and liver blood flow, molecular and cellular dynamics); gravitation, integrable systems; mathematical modelling; applied partial differential equations; numerical analysis and scientific computing; financial mathematics
• Pure mathematics : functional analysis; real and complex analysis; spectral theory; combinatorics; algebraic number theory; geometric topology; discrete and convex geometry; probability theory; geometric group theory; symplectic and contact topology

Research environment

The department is home to many internationally renowned mathematicians. We are delighted to be among the strongest mathematical science departments in the UK. In the Research excellence Framework 2021, UCL Mathematical Sciences was ranked 5th in the UK in terms of the number of papers ranked 3* or 4*. The expertise of our faculty covers the range of pure and applied mathematics with particular highlights including our leadership of the London School of Geometry and Number Theory which offers outstanding opportunities to early career young researchers in these fields. Numerous subject specific college seminars as well as intercollegiate seminars ensure that all PhD students have access to cutting edge research in their field.

Your primary activity in all years of study is to pursue research on your chosen research topic. This is conducted in close consultation with your primary supervisor.

During the first year you will usually take four courses from the inter-collegiate London Taught Course Centre. 

At or near the start of the second year students you will submit an upgrade report that is examined by a viva voce. On successful completion of this upgrade you will move from "MPhil" to "PhD" status.

Your primary activity in all years of study is to pursue research on your chosen research topic. This is conducted in close consultation with your primary supervisor. During the first two years you will usually take four courses from the inter-collegiate London Taught Course Centre. At or near the end of the third year students will submit an upgrade report that is examined by a viva voce. On successful completion of this upgrade you will move from MPhil to PhD status.

Accessibility

Details of the accessibility of UCL buildings can be obtained from AccessAble accessable.co.uk . Further information can also be obtained from the UCL Student Support and Wellbeing team .

Fees and funding

Fees for this course.

The tuition fees shown are for the year indicated above. Fees for subsequent years may increase or otherwise vary. Where the programme is offered on a flexible/modular basis, fees are charged pro-rata to the appropriate full-time Master's fee taken in an academic session. Further information on fee status, fee increases and the fee schedule can be viewed on the UCL Students website: ucl.ac.uk/students/fees .

Additional costs

Funded PhD places include the provision of a laptop by the department to be purchased in the first 2 years of studies. Students own the laptop and are, therefore, expected to pay the costs of insuring and backing-up their laptop. Students who leave their studies early are expected to return their laptop if already purchased.

For more information on additional costs for prospective students please go to our estimated cost of essential expenditure at Accommodation and living costs .

Funding your studies

For MPhil/PhD research at least two EPSRC doctoral training awards are normally offered each year. Approximately seven PhD teaching assistantships are also available each year. In addition, there are UCL Graduate Research Scholarships and Overseas Research Scholarships, and small departmental scholarships for which applicants are automatically considered on accepting an offer of a place.

Further opportunities for financial support are occasionally available. The department encourages and offers financial support for conference and workshop attendance.

For a comprehensive list of the funding opportunities available at UCL, including funding relevant to your nationality, please visit the Scholarships and Funding website .

CSC-UCL Joint Research Scholarship

Value: Fees, maintenance and travel (Duration of programme) Criteria Based on academic merit Eligibility: EU, Overseas

Deadlines and start dates are usually dictated by funding arrangements so check with the department or academic unit to see if you need to consider these in your application preparation. In most cases you should identify and contact potential supervisors before making your application. For more information see our How to apply page.

Please note that you may submit applications for a maximum of two graduate programmes (or one application for the Law LLM) in any application cycle.

Choose your programme

Please read the Application Guidance before proceeding with your application.

Year of entry: 2024-2025

Got questions get in touch.

Mathematics

[email protected]

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Mathematics PhD

• Full-time: Up to 4 years
• Part-time: Up to 8 years
• Start date: Multiple available
• UK fees: £5,350
• International fees: £23,000

Research overview

Follow your passion for research Join the School of Mathematical Sciences for the chance to work on projects in both fundamental and applied mathematical sciences that have an impact in the modern world. Projects cover the areas of:

• Pure mathematics
• Applied mathematics
• Mathematical physics
• Statistics and probability
• Mathematical education & scholarship.

Why choose Nottingham for your PhD? We're looking for passionate research students to help us shape the future of mathematical sciences and make a difference to the world around us.

Our research projects range from proposing new mathematical structures and uncovering new fundamental physics, to using mathematical sciences to produce sustainable materials, enhance future healthcare, and develop artificial intelligence.

Work is organised around exciting research themes, some of which focus on more traditional areas and others target emerging and multi-disciplinary problems:

• algebra, arithmetic, and their geometries
• computational statistics and machine learning
• data-driven modelling and computation
• epidemic modelling
• fluid mechanics
• geometry and symmetry
• mathematical medicine and biology
• mathematical neuroscience
• multiscale modelling and heterogeneous media
• numerical and applied analysis
• quantum information and metrology
• quantum mathematics
• real, complex and functional analysis
• symbolic computational mathematics
• teaching and learning in mathematics higher education
• wave modelling

Find out more about our research:

https://www.nottingham.ac.uk/mathematics/research/research.aspx

Research Excellence Framework 2021

• 97% of our research outputs are rated as 'world-leading' or 'internationally excellent'
• The school was placed in the top 3 for quality of research environment across all mathematical sciences units in the UK
• 100% of the impact from the school is rated as either ‘world-leading’ or ‘internationally excellent’

This is highlighted in our commitment to attracting bright minds and inspiring academics to conduct mathematical research throughout the department.

Find out how our mathematical research is revolutionising the global testing of future drug use

https://www.nottingham.ac.uk/vision/making-new-medicines-safer

Course content

Throughout your PhD you will focus on learning what information is already published and identifying gaps in knowledge. You will start to formulate your own research questions and develop skills to become a professional researcher.

• Study the research literature in your field, guided by your PhD advisor
• Attend seminars on modern research
• Take additional training in mathematical sciences and research skills
• Conduct research and obtain novel results
• Be part of an active and welcoming community of research students
• Write annual reports and journal publications to communicate your research findings
• Complete a written thesis of up to 100,000 words
• Take a verbal examination (viva voce) where you defend your research to an expert examination panel

The emphasis is on both broadening your knowledge base and improving the skills and techniques relevant for doing research on thesis-specific matters.

The PhD programme includes a training element, which may include research work as well as traditional taught material, and will include assessed components, designed to support your research.

In each year you will have a regular meetings with your supervisor and an annual review.

Entry requirements

All candidates are considered on an individual basis and we accept a broad range of qualifications. The entrance requirements below apply to 2025 entry.

Meeting our English language requirements

If you need support to meet the required level, you may be able to attend a presessional English course. Presessional courses teach you academic skills in addition to English language. Our  Centre for English Language Education is accredited by the British Council for the teaching of English in the UK.

If you successfully complete your presessional course to the required level, you can then progress to your degree course. This means that you won't need to retake IELTS or equivalent.

For on-campus presessional English courses, you must take IELTS for UKVI to meet visa regulations. For online presessional courses, see our CELE webpages for guidance.

Visa restrictions

International students must have valid UK immigration permissions for any courses or study period where teaching takes place in the UK. Student route visas can be issued for eligible students studying full-time courses. The University of Nottingham does not sponsor a student visa for students studying part-time courses. The Standard Visitor visa route is not appropriate in all cases. Please contact the university’s Visa and Immigration team if you need advice about your visa options.

We recognise that applicants have a variety of experiences and follow different pathways to postgraduate study.

We treat all applicants with alternative qualifications on an individual basis. We may also consider relevant work experience.

If you are unsure whether your qualifications or work experience are relevant, contact us .

How to indicate your research interests

You do not need to submit a detailed proposal, but you *must* indicate a research theme(s) , or Centre of Excellence that interests you and/or name specific academic staff members who could be your potential project supervisor and/or name specific projects.

• View our research themes >
• View our current research projects >

Further information required when applying

• Brief motivation for doing a PhD
• Your academic record and research experience
• Sources of funding (if applicable)

Application process and deadlines

We encourage applicants to apply before early to have the best chances of being awarded a fully-funded PhD scholarship (covers stipend and fees).

Stage 1 : Your application is assessed, and if successful, you will be invited for an interview. This is a video call or in person, if possible

Stage 2 : If successful at the interview stage, you will be considered for a fully-funded PhD scholarship.

When will you know if scholarship awarded?

• If applied before 7 January, result will be known around mid-February
• Late applications will be considered in subsequent rounds, with results known around mid April (if applied by 7 March) , and mid-June (if applied by 7 May ), and possibly later rounds depending on remaining available scholarships.

If you have funding support, intend to apply for an external scholarship, or are self-funded, you can apply throughout the year. Please indicate your funding details clearly in your application.

Study duration

Our standard duration of study is 3.5 years, although 3 or 4 year study is also available in some cases.

Our step-by-step guide contains everything you need to know about applying for postgraduate research.

Additional information for international students

If you are a student from the EU, EEA or Switzerland, you may be asked to complete a fee status questionnaire and your answers will be assessed using guidance issued by the UK Council for International Student Affairs (UKCISA) .

These fees are for full-time study. If you are studying part-time, you will be charged a proportion of this fee each year (subject to inflation).

Additional costs

All students will need at least one device to approve security access requests via Multi-Factor Authentication (MFA). We also recommend students have a suitable laptop to work both on and off-campus. For more information, please check the equipment advice .

We do not anticipate any extra significant costs, alongside your tuition fees and living expenses. You should be able to access most of the books and journals you’ll need through our libraries.

We offer a number of projects each year for which scholarship funding are available, including from the Engineering and Physical Sciences Research Council ( EPSRC ) and the University.

First class or distinction results are required as a minimum for funding.

There are many ways to fund your research degree, from scholarships to government loans.

Check our guide to find out more about funding your postgraduate degree.

Student support

The School of Mathematical Sciences provides dedicated support to its postgraduate researchers, including:

• Access to an appropriate personal computer
• Financial support to attend conferences and workshops
• Opportunity to earn extra money by supporting our teaching with demonstrating and marking
• You have a right to holiday leave, sick leave, and maternity/parental leave. You may also be able to switch to part-time (50%) PhD, depending on the approval of your funder

Wellbeing support

Your supervisors will support you throughout your research period. There is also further support within the school including:

• Mentoring system amongst research students
• Mentoring system between research students and postdoctoral research fellows
• Mental health support in the form of regular meetings for research students only
• Dedicated contacts for Support and Wellbeing, and for PGR Student Advice

To support training and learning, the school has access to specialised mathematical training courses provided by MAGIC (one of six Taught Course Centres supporting PhD mathematics programmes in the UK). Students can also utilise the Academy for PhD Training in Statistics (APTS).

Researcher training and development

The Researcher Academy is the network for researchers, and staff who support them. We work together to promote a healthy research culture, to cultivate researcher excellence, and develop creative partnerships that enable researchers to flourish.

Postgraduate researchers at Nottingham have access to our online Members’ area, which includes a wealth of resources, access to training courses and award-winning postgraduate placements.

You will have access to a range of support services , including:

• academic and disability support
• childcare services
• counselling service
• faith support
• financial support
• mental health and wellbeing support
• visa and immigration advice
• welfare support

Students' Union

Our Students' Union represents all students. You can join the Postgraduate Students’ Network or contact the dedicated Postgraduate Officer .

There are also a range of support networks, including groups for:

• international students
• black and minority ethnic students
• students who identify as women
• students with disabilities
• LGBT+ students

SU Advice provides free, independent and confidential advice on issues such as accommodation, financial and academic difficulties.

Where you will learn

Computer facilities.

The University provides excellent computing facilities with access to specialist mathematical software. The computers have electronic links to a high performance computing facility and specialist mathematical software such as Matlab, Mathematica and Maple.

University Park Campus

University Park Campus  covers 300 acres, with green spaces, wildlife, period buildings and modern facilities. It is one of the UK's most beautiful and sustainable campuses, winning a national Green Flag award every year since 2003.

Most schools and departments are based here. You will have access to libraries, shops, cafes, the Students’ Union, sports village and a health centre.

You can walk or cycle around campus. Free hopper buses connect you to our other campuses. Nottingham city centre is 15 minutes away by public bus or tram.

Jubilee Campus

Jubilee Campus has eco-friendly buildings, alongside green spaces, wildlife and a lake. 

This campus is home to our business, education and computer science schools, as well as a sports centre and student accommodation.

You can walk to  University Park Campus  in around 20 minutes or catch a free hopper bus. Nottingham city centre is 20 minutes away by public bus.

Furnished offices

As a research student here you will benefit from use of a furnished office which you'll share with other PhD students. You'll be provided with your own desk and personal computer or laptop and may make full use of general school facilities, including the common room, shared with academic staff.

The mathematics building benefits from lots of open space for discussion with staff and students and most of the supervisors are based in the same building too.

Whether you are considering a career in academia, industry or haven't yet decided, we’re here to support you every step of the way.

Expert staff will work with you to explore PhD career options and apply for vacancies, develop your interview skills and meet employers. You can book a one-to-one appointment, take an online course or attend a workshop.

International students who complete an eligible degree programme in the UK on a student visa can apply to stay and work in the UK after their course under the Graduate immigration route . Eligible courses at the University of Nottingham include bachelors, masters and research degrees, and PGCE courses.

Many of our PhD graduates move on to successful academic careers (e.g. Professor Caucher Birkar, recipient of the Fields Medal in 2018). Other choose to pursue exciting opportunities outside academia. PhD graduates in mathematics are in great demand in several sectors, including banking, finance, consulting, data analysis, and various types of industrial research.

Some of our PhD graduates have taken up roles such as:

• Assistant Professor
• Mathematical Modeller
• Project leader
• Post-doctoral researcher
• Research scientist
• Statistician

They work for organisations such as:

• Amey Strategic Consulting
• Francis Crick Institute

Related courses

Computer science phd, physics phd/mres, economics mres/phd, research excellence framework.

The University of Nottingham is ranked 7th in the UK for research power, according to analysis by Times Higher Education. The Research Excellence Framework (REF) is a national assessment of the quality of research in UK higher education institutions.

• We are ranked 13th in the UK for research power according to analysis by Times Higher Education, which takes into account a combination of the quality of our research, its international impact, critical mass and sustainability.
• 98% of our research is classed as ‘world-leading’ (4*) or ‘internationally excellent’ (3*).
• Places our school joint 3rd for quality of research environment across all Mathematical Sciences units in the UK based on % of 4 star research
• 90%* of our research is classed as 'world-leading' (4*) or 'internationally excellent' (3*)
• 100%* of our research is recognised internationally
• 51% of our research is assessed as 'world-leading' (4*) for its impact**

*According to analysis by Times Higher Education ** According to our own analysis.

This content was last updated on 01 July 2024 . Every effort has been made to ensure that this information is accurate, but changes are likely to occur between the date of publishing and course start date. It is therefore very important to check this website for any updates before you apply.

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MPhil/PhD Mathematics

• Graduate research
• Department of Mathematics
• Application code G1ZM
• Starting 2024
• Home full-time: Closed
• Overseas full-time: Closed
• Location: Houghton Street, London

This programme offers the chance to undertake a substantial piece of work that is worthy of publication and which makes an original contribution to the field of mathematics within our four broad disciplines – discrete mathematics and algorithms, financial mathematics and control theory, game theory, and operations research. You will begin on the MPhil, and will need to meet certain requirements to be upgraded to PhD status.

You have a plethora of topics to choose from including combinatorics, combinatorial optimisation, computational learning theory, control theory, financial mathematics, game theory, graph theory, integer programming, mechanism design, polyhedral combinatorics, probabilistic analysis, theory of computation and algorithms, and in the applications of mathematics in areas such as inspections, network optimisation, telecommunications, transportation, and economics.

Over the course of the years, the Department organises a number of personal development workshops for PhD students, designed to provide tailored support for specific areas of interest, such as careers, impact, and final year processes. Crucially, we have close ties with other departments at LSE, such as Statistics, Finance, Economics and Management, and we are an integral part of the mathematical community of the University of London.

All research students in the Department are provided with some funding each year to encourage and support their research activities, such as conference attendance and purchasing books and technology. Additional research funds are also available, upon application.

Programme details

For more information about tuition fees and entry requirements, see the fees and funding and assessing your application sections.

Entry requirements

Minimum entry requirements for mphil/phd mathematics.

Merit in a taught master's degree (or equivalent) in a related discipline and a 2:1 degree or equivalent in mathematics. 

Competition for places at the School is high. This means that even if you meet our minimum entry requirement, this does not guarantee you an offer of admission. 

If you have studied or are studying outside of the UK then have a look at our  Information for International Students  to find out the entry requirements that apply to you.

LSE values diversity and strives to promote equality at all levels. We strongly encourage applications from women, ethnic minorities, and members of other groups under-represented in higher education.

Assessing your application

Making an application.

We carefully consider each application on an individual basis, taking into account all the information presented on your application form, including your:

- academic achievement (including existing and pending qualifications) - CV - statement of academic purpose - outline research proposal - sample of written work - references

In addition to the general guidelines on application documents available  here , you can find specific guidelines for some of the application documents required as part of your application for the MPhil/PhD Mathematics programme below.  

Academic Achievement Provide detailed transcripts, with individual marks for all courses on your undergraduate and postgraduate degree programmes you have completed, and any available/provisional marks obtained in your current degree programme.

CV - Provide details of your education history. - Provide details of any employment history or other professional experience, including internships or volunteering activities. - Mention any relevant prior research experience, such as thesis work, research projects.    - If relevant, mention any career breaks or career changes, for example due to caring responsibilities.

Statement of Academic Purpose (1 page) - Explain your motivation for doing a PhD. - Explain your current career goals and aspirations and clarify how the PhD programme might help you realise them.  

Outline Research Proposal (1-2 pages) Many applicants will have little or no prior experience of research and therefore we do not expect a fully developed research proposal. The following is a recommendation of what to address, in a concise manner, in the research proposal. - Explain which overall research area you are interested in and explain why.  - Provide an example of one or two research papers that you have read or open problems you have heard about (in your proposed research area) and explain why you found them interesting. - Clarify who you see as potential supervisors and explain why.  - Explain how your training and skills are suitable for conducting research in your area of interest. For example, provide specific examples of related courses you have taken, and any research, internship, or work experiences that are relevant to your research area of interest. - If applicable, describe how any dissertation work from your BSc or MSc is relevant to your planned PhD research (be aware that this research will most likely be different).

Sample of Written Work (at least 5 pages) Submit something that showcases your mathematical writing. This could for example be a thesis, a project report, or some detailed exercise solutions. We like to see a writing sample that contains both mathematical details and plain text in which you discuss/interpret/explain the mathematical results. You can submit more than one writing sample if you only have short pieces of written work.

References You will need to nominate two referees. Academic referees are preferred, i.e., people who have taught you at university level.

If you can find a referee who can specifically comment on your research potential and your academic background in your chosen research area, that would be helpful. If you have any previous research experience, you could ask supervisors/project partners for a reference letter. An academic reference from your current degree programme where you already took exams are usually most helpful. If you have not taken any exams in your current programme yet, you can also ask for reference letters from previous degrees.

The referees will be asked to provide a reference letter and answer a selection of multiple-choice questions in which they will need to provide an assessment of your academic performance/potential etc. and research potential. --------------

Completed applications are sent to the Department after they are processed by the Graduate Admissions Office. In the Department, the numbers and quality of competing applications and the availability of an appropriate supervisor are considered. If your application is shortlisted for consideration, an interview will be arranged with the appropriate members of staff by telephone or video conferencing software. Once all interviews have been conducted, the Department will decide on who to accept and who to offer funding. If your application is received before the deadline, we aim to notify you about the outcome by the end of Winter Term.

You may also have to provide evidence of your English proficiency. You do not need to provide this at the time of your application to LSE, but we recommend that you do see our  English language requirements  for further information.

When to apply

The application deadline for this programme is 23 May 2024 . However, to be considered for any LSE funding opportunity, you must have submitted your application and all supporting documents by the funding deadline. See the fees and funding section for more details.

Fees and funding

Every research student is charged a fee in line with the fee structure for their programme. The fee covers registration and examination fees payable to the School, lectures, classes and individual supervision, lectures given at other colleges under intercollegiate arrangements and, under current arrangements, membership of the Students' Union. It does not cover living costs or travel or fieldwork.

Tuition fees 2024/25 for MPhil/PhD Mathematics

Home students: £4,786 for the first year Overseas students: £22,632 for the first year

The fee is likely to rise over subsequent years of the programme. The School charges home research students in line with the level of fee that the Research Councils recommend. The fees for overseas students are likely to rise in line with the assumed percentage increase in pay costs (ie, 4 per cent per annum).

The Table of Fees shows the latest tuition amounts for all programmes offered by the School.

The amount of tuition fees you will need to pay, and any financial support you are eligible for, will depend on whether you are classified as a home or overseas student, otherwise known as your fee status. LSE assesses your fee status based on guidelines provided by the Department of Education.

Further information about fee status classification.

Scholarships, studentships and other funding

The School recognises that the  cost of living in London  may be higher than in your home town or country, and we provide generous scholarships each year to home and overseas students.

This programme is eligible for  LSE PhD Studentships and  Economic and Social Research Council (ESRC) funding . Selection for the PhD Studentships and ESRC funding is based on receipt of an application for a place – including all ancillary documents, before the funding deadline.

Funding deadline for LSE PhD Studentships: 15 January 2024

In addition to our needs-based awards, LSE also makes available scholarships for students from specific regions of the world and awards for students studying specific subject areas.  Find out more about financial support.

In addition, students on this programme are eligible for the Department of Mathematics' PhD Prize for Outstanding Academic Performance , which is an annual award for the best PhD performance from a student completing in the previous academic year.

External funding 

There may be other funding opportunities available through other organisations or governments and we recommend you investigate these options as well. 

Further information

Fees and funding opportunities

Information for international students

LSE is an international community, with over 140 nationalities represented amongst its student body. We celebrate this diversity through everything we do.  

If you are applying to LSE from outside of the UK then take a look at our Information for International students . 

1) Take a note of the UK qualifications we require for your programme of interest (found in the ‘Entry requirements’ section of this page). 

2) Go to the International Students section of our website. 

3) Select your country. 

4) Select ‘Graduate entry requirements’ and scroll until you arrive at the information about your local/national qualification. Compare the stated UK entry requirements listed on this page with the local/national entry requirement listed on your country specific page.

Programme structure and courses

In addition to progressing with your research, you are expected to take the listed training and transferable skills courses. You may take courses in addition to those listed and should discuss this with your supervisor. At the end of your second year (full-time), you will need to satisfy certain requirements, and if you meet these, will be retroactively upgraded to PhD status.

Training courses – Compulsory (not examined) Courses designed for research in Mathematics need to be chosen in consultation with your lead supervisor. Discrete Mathematics and Algorithms, Operations Research and Game Theory students will attend four courses organised by the London Taught Course Centre .

There are separate arrangements for students in Financial Mathematics, where courses are provided by the London Graduate School in Mathematical Finance . You also have the option of attending or auditing LSE Taught Masters modules, where appropriate.

Transferable skills courses – Compulsory (not examined) Mathematics: Seminar on Combinatorics, Games and Optimisation Research Student Seminar – you must attend and make presentations

Second year

Transferable skills courses – Compulsory (not examined) Mathematics Seminar Research Student Seminar - you must attend and make presentations.

Transferable skills courses – Compulsory (not examined) Mathematics Seminar Research Student Seminar - you must attend and make presentations.

Fourth year

Transferable skills courses– Compulsory (not examined) Mathematics Seminar Research Student Seminar - you must attend and make presentations.

For the most up-to-date list of optional courses please visit the relevant School Calendar page .  

You must note, however, that while care has been taken to ensure that this information is up to date and correct, a change of circumstances since publication may cause the School to change, suspend or withdraw a course or programme of study, or change the fees that apply to it. The School will always notify the affected parties as early as practicably possible and propose any viable and relevant alternative options. Note that the School will neither be liable for information that after publication becomes inaccurate or irrelevant, nor for changing, suspending or withdrawing a course or programme of study due to events outside of its control, which includes but is not limited to a lack of demand for a course or programme of study, industrial action, fire, flood or other environmental or physical damage to premises.  

You must also note that places are limited on some courses and/or subject to specific entry requirements. The School cannot therefore guarantee you a place. Please note that changes to programmes and courses can sometimes occur after you have accepted your offer of a place. These changes are normally made in light of developments in the discipline or path-breaking research, or on the basis of student feedback. Changes can take the form of altered course content, teaching formats or assessment modes. Any such changes are intended to enhance the student learning experience. You should visit the School’s  Calendar , or contact the relevant academic department, for information on the availability and/or content of courses and programmes of study. Certain substantive changes will be listed on the  updated graduate course and programme information page.

Supervision, progression and assessment

Supervision.

Supervisors are selected during the application process, where we take into account the information and preferences you mention in your application. You will be assigned to:

-  One or two principal supervisor(s) with requisite knowledge in your chosen field. Most of your day-to-day supervision will be with the principal supervisor(s). If the research project or your interests shift during your time in the Department, it is possible to change principal supervisor(s). - If there is only one principal supervisor, an appropriate second supervisor will be appointed. There will always be a principal supervisor from the Mathematics Department. Where appropriate, a second or joint supervisor may be appointed from another department or institution.

Progression and assessment

You are initially registered for the MPhil, and will be able to upgrade to PhD registration during your second year, dependent on satisfactory progress. Progress is assessed regularly by your supervisors, in consultation with the Doctoral Programme Director, on the basis of the extent to which the agreed research goals have been achieved. Any upgrade is dependent on the successful completion of a Major Review, the date of which is determined by the Doctoral Programme Director in consultation with the lead supervisor.

By the end of your first year you will be required to present a more detailed project proposal. The proposal, which should illustrate your command of the theoretical and empirical literature related to your topic, will be a clear statement of the theoretical and methodological approach you will take. It will include a draft outline and work plan, which should identify any periods of fieldwork necessary to your research. This should demonstrate the coherence and feasibility of the proposed research and thesis.

Study facilities

Students are provided with their own workspace and Windows PC within the Department of Mathematics’ PhD study room.  This area was recently renovated, and has been modernised to become a professional, purposeful, and relaxed work environment. Students are thus offered a supportive environment within a community of scholars and are well-placed to pursue a career building on their research accomplishments. 

In addition to the space provided in Columbia House, a dedicated Postgraduate Common Room is available to students in 32 Lincoln's Inn Fields.  Students will also find the  PhD Academy  useful, a dedicated space and services hub for doctoral candidates.

Students will have access to the comprehensive facilities of the  LSE Library  and to the libraries of other colleges of the University of London. They will also benefit from the IT and other facilities available at the School.

Student support and resources

We’re here to help and support you throughout your time at LSE, whether you need help with your academic studies, support with your welfare and wellbeing or simply to develop on a personal and professional level.

Whatever your query, big or small, there are a range of people you can speak to who will be happy to help.  

Department librarians   – they will be able to help you navigate the library and maximise its resources during your studies. 

Accommodation service  – they can offer advice on living in halls and offer guidance on private accommodation related queries.

Class teachers and seminar leaders  – they will be able to assist with queries relating to specific courses. 

Disability and Wellbeing Service  – they are experts in long-term health conditions, sensory impairments, mental health and specific learning difficulties. They offer confidential and free services such as  student counselling,  a  peer support scheme  and arranging  exam adjustments.  They run groups and workshops.  

IT help  – support is available 24 hours a day to assist with all your technology queries.   

LSE Faith Centre  – this is home to LSE's diverse religious activities and transformational interfaith leadership programmes, as well as a space for worship, prayer and quiet reflection. It includes Islamic prayer rooms and a main space for worship. It is also a space for wellbeing classes on campus and is open to all students and staff from all faiths and none.   

Language Centre  – the Centre specialises in offering language courses targeted to the needs of students and practitioners in the social sciences. We offer pre-course English for Academic Purposes programmes; English language support during your studies; modern language courses in nine languages; proofreading, translation and document authentication; and language learning community activities.

LSE Careers  ­ – with the help of LSE Careers, you can make the most of the opportunities that London has to offer. Whatever your career plans, LSE Careers will work with you, connecting you to opportunities and experiences from internships and volunteering to networking events and employer and alumni insights. 

LSE Library   –   founded in 1896, the British Library of Political and Economic Science is the major international library of the social sciences. It stays open late, has lots of excellent resources and is a great place to study. As an LSE student, you’ll have access to a number of other academic libraries in Greater London and nationwide. 

LSE LIFE  – this is where you should go to develop skills you’ll use as a student and beyond. The centre runs talks and workshops on skills you’ll find useful in the classroom; offers one-to-one sessions with study advisers who can help you with reading, making notes, writing, research and exam revision; and provides drop-in sessions for academic and personal support. (See ‘Teaching and assessment’). 

LSE Students’ Union (LSESU)  – they offer academic, personal and financial advice and funding.  

PhD Academy   – this is available for PhD students, wherever they are, to take part in interdisciplinary events and other professional development activities and access all the services related to their registration. 

Sardinia House Dental Practice   – this   offers discounted private dental services to LSE students.  

St Philips Medical Centre  – based in Pethwick-Lawrence House, the Centre provides NHS Primary Care services to registered patients.

Student Services Centre  – our staff here can answer general queries and can point you in the direction of other LSE services.  

Student advisers   – we have a  Deputy Head of Student Services (Advice and Policy)  and an  Adviser to Women Students  who can help with academic and pastoral matters.

Student life

As a student at LSE you’ll be based at our central London campus. Find out what our campus and London have to offer you on academic, social and career perspective. 

Student societies and activities

Your time at LSE is not just about studying, there are plenty of ways to get involved in  extracurricular activities . From joining one of over 200 societies, or starting your own society, to volunteering for a local charity, or attending a public lecture by a world-leading figure, there is a lot to choose from. 

The campus 

LSE is based on one  campus  in the centre of London. Despite the busy feel of the surrounding area, many of the streets around campus are pedestrianised, meaning the campus feels like a real community. 

Life in London 

London is an exciting, vibrant and colourful city. It's also an academic city, with more than 400,000 university students. Whatever your interests or appetite you will find something to suit your palate and pocket in this truly international capital. Make the most of career opportunities and social activities, theatre, museums, music and more. 

Want to find out more? Read why we think  London is a fantastic student city , find out about  key sights, places and experiences for new Londoners . Don't fear, London doesn't have to be super expensive: hear about  London on a budget . 

Student stories

To read all our Alumni Stories,  see our webpage here .

Quick Careers Facts for the Department of Mathematics

Median salary of our PG students 15 months after graduating: £39,500

• Financial and Professional Services              
• Information, Digital Technology and Data            
• Accounting and Auditing              
• Real Estate, Environment and Energy 
• Advertising, Marketing, PR, Media, Entertainment, Publishing and Journalism

Top 5 sectors our students work in:

The data was collected as part of the Graduate Outcomes survey, which is administered by the Higher Education Statistics Agency (HESA). Graduates from 2020-21 were the fourth group to be asked to respond to Graduate Outcomes. Median salaries are calculated for respondents who are paid in UK pounds sterling and who were working in full-time employment.

Students who successfully complete the programme often embark on an academic career. 

Further information on graduate destinations for this programme

Support for your career

Many leading organisations give careers presentations at the School during the year, and LSE Careers has a wide range of resources available to assist students in their job search. Find out more about the  support available to students through LSE Careers .

Frequently Asked Questions

Can i or must i teach as a mphil/phd student in the department.

All mathematics MPhil/PhD students are usually expected to undertake some class teaching for the Department. You will be paid separately for this. Further details will be provided on your arrival. 

Will I receive any additional funding to support conference attendance, book purchases, etc.?

Each registered PhD student in the Department is entitled to claim up to £500 per academic year towards their research expenses relating directly to your studies, such as the purchase of books or conference attendance. All claims must be accompanied by full receipts. 

Can I apply to start in the Winter Term (January) or Spring Term (April)?

Under execptional circumstances, starting in January may be permissable.  Starting in the Spring Term is not permitted.

I am already enrolled in a PhD programme at another university and I would like to transfer to your PhD programme. How do I do that?

LSE does not accept transfer of credits. All MPhil/PhD applicants, regardless of previous academic experience, are required to complete a formal application. Previous research will be considered, but all students are initially registered as MPhil students by the School, are upgraded to PhD status according to the Department's standard policy and are required to fulfil the School's minimum registration requirements.

Can I apply to study part-time?

We will consider applications for part-time registrations in the PhD programme, subject to visa regulations. Applicants with personal circumstances such as caring responsibilities who may otherwise not pursue a PhD may consider this route. We emphasise that studying for a PhD requires a serious commitment of regular periods of time and concentration. Pursuing a PhD while holding full-time employment is discouraged.

We would need to see evidence that an applicant:

• Would be available to participate in activities that are essential to becoming an independent researcher (e.g. attend seminars, go to conferences, follow taught courses in their first year(s), etc.)
• Can find mutual times to work with their proposed supervisor
• Can spend sufficient time on their PhD research

Find out more about LSE

Discover more about being an LSE student - meet us in a city near you, visit our campus or experience LSE from home. 

Experience LSE from home

Webinars, videos, student blogs and student video diaries will help you gain an insight into what it's like to study at LSE for those that aren't able to make it to our campus.  Experience LSE from home . 

Come on a guided campus tour, attend an undergraduate open day, drop into our office or go on a self-guided tour.  Find out about opportunities to visit LSE . 

LSE visits you

Student Marketing, Recruitment and Study Abroad travels throughout the UK and around the world to meet with prospective students. We visit schools, attend education fairs and also hold Destination LSE events: pre-departure events for offer holders.  Find details on LSE's upcoming visits . 

How to apply

Virtual Graduate Open Day

Register your interest

Related programmes, mphil/phd statistics.

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School of Mathematics

PhD in Mathematics

We are proud of our world-class reputation for research excellence and our commitment to provide the highest quality training for our postgraduate students.

The School of Mathematics offers a cutting-edge PhD programme, and we welcome applications from national and international students all year round. Our postgraduate students enjoy a friendly and stimulating environment, and during your PhD you will have the opportunity to develop your mathematical research skills, collaborate with leading researchers and apply your expertise across a range of academic areas.

Research Areas

Review our many research areas for detailed accounts of our various research themes and related academic staff.

Research Environment

Discover our PhD research environment and the various opportunities offered to our research students.

PhD Projects

View some of the PhD projects, offered by our academics for 2024/25 academic year. 

Funding Opportunities

To receive full consideration for funding for our programme commencing September 2024, applications should be submitted before 5 January 2024.

Project-specific funding opportunities may have later application deadlines, please see the PhD Project pages for further details.

Please note that we are not able to consider applications submitted after the programme is full.

Read our Prospectus

Find out more about the programme including entry requirements and fees.

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When you’re doing research, you can direct it yourself; you have more freedom. It's the only thing I can imagine myself doing.

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Our Graduate School is supervised by internationally-leading researchers spanning a wide spectrum of topics, making our School a world renowned centre of excellence in mathematics.

Watch a recording of the School of Mathematics' Graduate School Virtual Open Day 20-21

The School of Mathematics welcomes applications to our Visitors Programme from research students who are registered at another university.

MAC-MIGS CDT

MAC-MIGS is a prestigious EPSRC-funded PhD programme in Mathematical Modelling, Analysis and Computation, run jointly by Edinburgh and Heriot-Watt universities, as part of the Maxwell Institute Graduate School, that offers fully-funded scholarships.

MAC-MIGS website

The Maxwell Institute Graduate School in Analysis and its Applications (MIGSAA) is a Centre for Doctoral Training that provides high quality instruction in analysis and the applications of analysis to a wide range of areas. MIGSAA has been made possible by a grant from the UK's Engineering and Physical Sciences Research Council and the Scottish Funding Council.

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PhD opportunities

Our PhD programme is your chance to join the next generation of world-class researchers in mathematics and statistics, to contribute to knowledge and develop transferable research skills.

We recognise barriers faced by under-represented groups, and encourage enquiries or applications from all qualified students with a love of mathematics and a strong desire to explore it further, as part of a welcoming and inclusive community.

Advice for PhD applicants

PhD student profiles

Our Research pages list the research interests and contact details of our academic staff: you can use these to get in touch and discuss PhD opportunities and potential projects in their field, some of which may be listed below.

You can find details of recent PhD theses completed in SoMaS, in the White Rose Repository, by inserting the following link:  https://etheses.whiterose.ac.uk/view/iau/Sheffield=2ESOM/

Projects may come with specific funding (for example, from a research council or Centre for Doctoral Training) to cover your tuition fees and living expenses. More often, this is not the case, but you may be able to  apply for a scholarship .

Once you have found a supervisor you wish to study with, find out  how to apply .

Our standard conditional offer is to require a UK First Class MMath or MSc Distinction (or international equivalent), in Mathematics or a relevant related subject. That is modified to 2.1 MMath or MSc Merit in the following research groups: Statistics, Solar Physics and Space Plasma Research Centre (SP2RC). It is modified to 1st BSc or MMath, or MSc Distinction, in the Probability research group

Our decision on whether to offer you a place will also be based on the research proposal or personal statement you submit, your degree transcripts (and certificates, if available), your masters dissertation/project (if applicable), your CV and academic references (including your masters dissertation/project supervisor, if applicable), and any interviews and additional tasks we ask you to complete.

All documents need to be provided in English, including transcripts and references.

Students will also need to meet our English language requirements , and international students may need to get clearance through the Academic Technology Approval Scheme (ATAS) .

If you would like any more information or have any questions, please email [email protected] .

Related information

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How to apply

Search for PhD opportunities at Sheffield and be part of our world-leading research.

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Various postgraduate courses of a mathematical nature are available at the University of Cambridge, including both taught courses and research degrees.

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We have 95 Mathematics (fully funded) PhD Projects, Programmes & Scholarships

Mathematics

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Mathematics (fully funded) PhD Projects, Programmes & Scholarships

Fully funded phd positions at the imt school for advanced studies lucca, funded phd programme (students worldwide).

Some or all of the PhD opportunities in this programme have funding attached. Applications for this programme are welcome from suitably qualified candidates worldwide. Funding may only be available to a limited set of nationalities and you should read the full programme details for further information.

Italy PhD Programme

An Italian PhD usually takes 3-4 years and consists of some taught units as well as research towards your thesis. This will be examined at a public defence, rather than a private viva voce. Some programmes are taught in English.

Fully funded PhD positions in Astronomy, Biology, Computer Science, Chemistry & Materials, Data Science & Scientific Computing, Earth Science, Mathematics, Neuroscience, and Physics

International phd programme.

International PhD programs are often designed for international students. Your PhD will usually be delivered in English, though some opportunities to gain and use additional language skills might also be available. Students may propose their own PhD topics or apply for advertised projects.

Fully funded EPSRC Centre for Doctoral Training (CDT) in Cyber Security

Funded phd programme (uk students only).

Some or all of the PhD opportunities in this programme have funding attached. It is only available to UK citizens or those who have been resident in the UK for a period of 3 years or more. Some projects, which are funded by charities or by the universities themselves may have more stringent restrictions.

EPSRC Centre for Doctoral Training

EPSRC Centres for Doctoral Training conduct research and training in priority areas funded by the UK Engineering and Physical Sciences Research Council. Potential PhD topics are usually defined in advance. Students may receive additional training and development opportunities as part of their programme.

Fully funded PhD studentships at the EPSRC Centre for Doctoral Training in Statistics and Operational Research in Partnership with Industry (STOR-i)

Fully funded 3-year ph.d. position in transportation engineering at the university of canterbury, new zealand, phd research project.

PhD Research Projects are advertised opportunities to examine a pre-defined topic or answer a stated research question. Some projects may also provide scope for you to propose your own ideas and approaches.

Funded PhD Project (Students Worldwide)

This project has funding attached, subject to eligibility criteria. Applications for the project are welcome from all suitably qualified candidates, but its funding may be restricted to a limited set of nationalities. You should check the project and department details for more information.

University of Edinburgh School of Mathematics fully funded PhD studentships

Maths research programme.

PhD Research Programmes describe the opportunities for postgraduate research within a University department. You may often be asked to submit your own research project proposal as part of your application, although predefined research projects may also be available.

Fully Funded Research Position in ‘Machine Learning for Autonomous Robot Exploration’

Funded phd project (european/uk students only).

This project has funding attached for UK and EU students, though the amount may depend on your nationality. Non-EU students may still be able to apply for the project provided they can find separate funding. You should check the project and department details for more information.

Fully Funded PhD Program Opportunity

Physics: fully funded swansea university and the university of edinburgh phd scholarship: lattice field theory going beyond the standard model, fully funded phd opportunities in maths and computing sciences, 4 year phd programme.

4 Year PhD Programmes are extended PhD opportunities that involve more training and preparation. You will usually complete taught courses in your first year (sometimes equivalent to a Masters in your subject) before choosing and proposing your research project. You will then research and submit your thesis in the normal way.

PhD Projects in Mathematics

Phd student positions at international max planck research school for molecules of life, munich, germany phd programme.

A German PhD usually takes 3-4 years. Traditional programmes focus on independent research, but more structured PhDs involve additional training units (worth 180-240 ECTS credits) as well as placement opportunities. Both options require you to produce a thesis and present it for examination. Many programmes are delivered in English.

Max Planck Research Programme

Max Planck Research Programmes are structured PhD opportunities set up by the Max Planck Society, an independent non-profit German research organisation. Max Planck Institutes and universities collaborate to offer interdisciplinary and international PhD opportunities providing high standards of training and support as well as generous funding.

Implementation of optimisation trials of complex health and social care interventions

Funded phd project (uk students only).

This research project has funding attached. It is only available to UK citizens or those who have been resident in the UK for a period of 3 years or more. Some projects, which are funded by charities or by the universities themselves may have more stringent restrictions.

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Mathematical Physics PhD

Awards: PhD

Study modes: Full-time, Part-time

Funding opportunities

Programme website: Mathematical Physics

Discovery Day

Join us online on 21st August to learn more about postgraduate study at Edinburgh.

Find out more and register

Research profile

We are a multidisciplinary research group with close connections with the School’s Algebra and Geometry & Topology groups.

You’ll benefit from being not only in one of the largest mathematics research groups in the UK but also part of the Edinburgh Mathematical Physics Group – a joint research collective formed in 1999 with Heriot- Watt University and now part of the Maxwell Institute.

The School of Mathematics is a vibrant community of more than 60 academic and related staff supervising 60 students.

Our group pursues wide-ranging interests spanning a number of disciplines. A central goal is to understand the principles behind quantum gravity, through the study of black holes, cosmologies and spacetime singularities, and via the use of holography and the interplay with quantum gauge field theory through the gauge/gravity correspondence.

Particularly fruitful areas of research are the geometry of higher-dimensional black holes and their near-horizon geometries in the context of higher-dimensional generalisations of general relativity.

We’re fascinated by the various manifestations of supersymmetry: in string theory, supergravity and gauge theory. This has led us to several classification results on supersymmetric supergravity backgrounds, including a recent proof of the homogeneity conjecture. In addition we study gauge theoretic moduli spaces using supersymmetry and via integrable systems techniques, displaying an interplay between the algebraic geometry of curves and their associated function theory. This research has led to computer implementations of various algebro-geometric constructions.

Recently we have made progress in some purely mathematical problems suggested by the gauge/gravity correspondence: namely, the classification of certain exotic algebraic structures related to superconformal field theories, as well as that of certain types of homogeneous supergravity backgrounds.

Training and support

Mathematics is a discipline of high intellect with connections stretching across all the scientific disciplines and beyond, and in Edinburgh you can be certain of thriving in a rich academic setting. Our School is one of the country’s largest mathematics research communities in its own right, but you will also benefit from Edinburgh’s high-level collaborations, both regional and international.

Research students will have a primary and secondary supervisor and the opportunity to network with a large and varied peer group. You will be carrying out your research in the company of eminent figures and be exposed to a steady stream of distinguished researchers from all over the world.

Our status as one of the most prestigious schools in the UK for mathematics attracts highly respected staff. Many of our 60 current academics are leaders in their fields and have been recognised with international awards.

Researchers are encouraged to travel and participate in conferences and seminars. You’ll also be in the right place in Edinburgh to meet distinguished researchers from all over the world who are attracted to conferences held at the School and the various collaborative centres based here. You’ll find opportunities for networking that could have far-reaching effects on your career in mathematics.

As well as experiencing a vibrant research environment that brings you into contact with a broad group of your peers, your membership of the Edinburgh Mathematical Physics Group will give you access to a dynamic programme of seminars, lecture courses and conferences. There is a dedicated website and blog, and a comprehensive range of graduate activities:

• Edinburgh Mathematical Physics Group

You will enjoy excellent facilities, ranging from one of the world’s major supercomputing hubs to libraries for research at the leading level, including the new Noreen and Kenneth Murray Library at King’s Buildings.

Students have access to more than 1,400 computers in suites distributed across our University’s sites, many of which are open 24 hours a day. In addition, if you are a research student, you will have access to dedicated desk space with monitors and a laptop computer.

We provide all our mathematics postgraduates with access to software packages such as:

• Mathematica

Research students are allocated parallel computing time on ‘Eddie’, the Edinburgh Compute and Data Facility. You can also request use of the BlueGene/Q supercomputer facility for your research.

Entry requirements

These entry requirements are for the 2024/25 academic year and requirements for future academic years may differ. Entry requirements for the 2025/26 academic year will be published on 1 Oct 2024.

A UK first class honours degree, or its international equivalent, in an appropriate subject; or a UK 2:1 honours degree plus a UK masters degree, or their international equivalents; or relevant qualifications and experience.

International qualifications

Check whether your international qualifications meet our general entry requirements:

• Entry requirements by country
• English language requirements

Regardless of your nationality or country of residence, you must demonstrate a level of English language competency at a level that will enable you to succeed in your studies.

English language tests

We accept the following English language qualifications at the grades specified:

• IELTS Academic: total 6.5 with at least 6.0 in each component. We do not accept IELTS One Skill Retake to meet our English language requirements.
• TOEFL-iBT (including Home Edition): total 92 with at least 20 in each component. We do not accept TOEFL MyBest Score to meet our English language requirements.
• C1 Advanced ( CAE ) / C2 Proficiency ( CPE ): total 176 with at least 169 in each component.
• Trinity ISE : ISE II with distinctions in all four components.
• PTE Academic: total 62 with at least 59 in each component.

Your English language qualification must be no more than three and a half years old from the start date of the programme you are applying to study, unless you are using IELTS , TOEFL, Trinity ISE or PTE , in which case it must be no more than two years old.

Degrees taught and assessed in English

We also accept an undergraduate or postgraduate degree that has been taught and assessed in English in a majority English speaking country, as defined by UK Visas and Immigration:

• UKVI list of majority English speaking countries

We also accept a degree that has been taught and assessed in English from a university on our list of approved universities in non-majority English speaking countries (non-MESC).

• Approved universities in non-MESC

If you are not a national of a majority English speaking country, then your degree must be no more than five years old* at the beginning of your programme of study. (*Revised 05 March 2024 to extend degree validity to five years.)

Find out more about our language requirements:

• Academic Technology Approval Scheme

If you are not an EU , EEA or Swiss national, you may need an Academic Technology Approval Scheme clearance certificate in order to study this programme.

Fees and costs

Tuition fees.

Scholarships and funding

Featured funding.

• School of Mathematics funding opportunities

UK government postgraduate loans

If you live in the UK, you may be able to apply for a postgraduate loan from one of the UK's governments.

The type and amount of financial support you are eligible for will depend on:

• your programme
• the duration of your studies
• your tuition fee status

Programmes studied on a part-time intermittent basis are not eligible.

• UK government and other external funding

Other funding opportunities

Search for scholarships and funding opportunities:

• Search for funding

Further information

• Graduate School Administrator
• Phone: +44 (0)131 650 5085
• Contact: [email protected]
• School of Mathematics
• James Clerk Maxwell Building
• Peter Guthrie Tait Road
• The King's Buildings Campus
• Programme: Mathematical Physics
• School: Mathematics
• College: Science & Engineering

Select your programme and preferred start date to begin your application.

PhD Mathematical Physics - 3 Years (Full-time)

Phd mathematical physics - 6 years (part-time), application deadlines.

We strongly recommend you submit your completed application as early as possible, particularly if you are also applying for funding or will require a visa. We may consider late applications if we have places available. All applications received by 22 January 2024 will receive full consideration for funding. Later applications will be considered until all positions are filled.

• How to apply

You must submit two references with your application.

Find out more about the general application process for postgraduate programmes:

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PhD studentships in mathematics

The Department of Mathematics at the University of Surrey is offering up to 4 fully funded PhD studentships across its vibrant research groups, which focus on topics such as data science, life and social sciences, fluid mechanics, dynamical systems and PDEs and mathematical physics.

Application deadline

Funding source, funding information.

Each PhD studentship is fully-funded, including fees and a tax-free stipend, at UKRI studentship rates covered for the duration of 3 to 4 years for UK candidates. International candidates are welcome to apply but will need to cover the difference between the UK and overseas fees.

The Department of Mathematics at the University of Surrey is offering up to four fully funded PhD studentships across its vibrant research groups, which focus on topics such as data science, life and social sciences, fluid mechanics, dynamical systems and PDEs and mathematical physics.

Successful applicants will be part of a strong research-focussed department consisting of internationally recognised potential supervisors, supported by a community of ambitious early career researchers. As a PhD student you will be extensively trained for a career as a professional mathematician, which will set you on the right track for a future in academia, industry or government.

During your PhD you will also receive a comprehensive training in professional skills such as project management, communication and time management through our Faculty Graduate School. In addition, you will broaden your mathematical horizons by taking courses via national networks such as the MAGIC consortium as well as our own in-house MSc programme.

We are seeking high-quality PhD candidates to work on research projects in all our research groups. Possible PhD projects include, but are not limited to, the following list:

• Data-driven modelling and machine learning for biological applications
• Mathematical modelling, data science or dynamical systems analysis of sleep regulation
• From signal processing to biology: Application of stochastic filtering to model bio-system dynamics
• Design of Experiments: investigation of observation loss in row column designs
• Incompressible buckling and non-uniqueness of minimizers in the Calculus of Variations.
• Attractor signatures from ECG data for the detection of arrhythmias
• Hydrodynamic models of hybrid quantum-classical systems
• Quantitative Systems Pharmacology: mechanistic models for pre-clinical cancer drug trials
• Massless scattering, spin-chains and thermodynamic Bethe ansatz in the integrable AdS3/CFT2 and AdS2/CFT1 correspondences
• Nonlinear structures in vortices with radial density variations.
• Analysis of `pressure functionals' and associated PDE in Nonlinear Elasticity

For information on other possible PhD research areas check out our research pages , and informal discussions with academics via email is encouraged. Get more information on the Mathematics PhD programme at Surrey.

Eligibility criteria

Applicants should have a minimum of a first class honours degree in mathematics, the physical sciences or engineering. Preferably applicants will hold a MMath, MPhys or MSc degree, though exceptional BSc students will be considered.

Available for UK students only.

English language requirements

IELTS requirements:  6.5 or above (or equivalent) with 6.0 in each individual category.

How to apply

To make a formal application you should complete the University online PhD application form . In the `Research Proposal’ document of the application form please discuss your favourite research areas, any research experience you may have, and your preferred PhD research area. Once your application is received, it is reviewed by the relevant academics, who may contact you to arrange a formal interview.

We place great value on equality, diversity and inclusion and welcome candidates from all backgrounds. We are seeking to increase the diversity within our community and would encourage applications from under-represented groups, including female candidates, people from Black, Asian and minority ethnic groups and people with disabilities. Studentships will always be offered on merit.

Informal applications about the application procedure can be made to the Mathematics Postgraduate Research Director via [email protected] .

Studentship FAQs

Read our  studentship FAQs  to find out more about applying and funding.

25 November 2022

Contact details

Cesare tronci.

Email:  [email protected]

Studentships at Surrey

We have a wide range of studentship opportunities available.

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Course closed:

Education (Mathematics Education) is no longer accepting new applications.

The Mathematics Education route is for anyone with a research or professional interest in mathematics education at any level of education (primary, secondary, or tertiary), wanting to undertake advanced study in a world-class setting. The Mathematics Education route is taught by a specialist team, and its student cohort is drawn primarily from UK-based professionals who continue in their full-time posts while taking the course part-time

The Mathematics Education route develops students' understanding of a number of important issues in the field of mathematics education. Students learn to interpret and critically engage with ideas and debates in mathematics education research in three ways:

• through taught sessions in mathematics education;
• through work on course assignments under the supervision of a member of the teaching team; and
• through participation in seminars led by students on the route and in project workshops.

The course introduces students to research skills and specialist knowledge. Its main aims are to:

• to examine the theoretical frameworks used in the study of education and its constituent disciplines;
• provide training in research methods appropriate to education;
• advance students’ capacity for professional reflection and judgment;
• cater for a range of specialists interested within the field of education or one of its constituent disciplines.

Learning Outcomes

By the end of the course, students will have:

• a comprehensive understanding of research techniques, and a thorough knowledge of the literature applicable to their specific educational domain;
• demonstrated originality in the application of knowledge, together with a practical understanding of how research and enquiry are used to create and interpret knowledge in their field;
• shown abilities in the critical evaluation of current research and research techniques and methodologies;
• demonstrated self-direction and originality in tackling and solving problems, and acted autonomously in the planning and implementation of research.

Continuation to the PhD from Masters programmes within the Faculty of Education is not automatic, and students wishing to do so must submit a PhD application by the usual deadline.

The Postgraduate Virtual Open Day usually takes place at the end of October. It’s a great opportunity to ask questions to admissions staff and academics, explore the Colleges virtually, and to find out more about courses, the application process and funding opportunities. Visit the  Postgraduate Open Day  page for more details.

See further the  Postgraduate Admissions Events  pages for other events relating to Postgraduate study, including study fairs, visits and international events.

Key Information

24 months part-time, study mode : taught, master of philosophy, faculty of education, course - related enquiries, application - related enquiries, course on department website, dates and deadlines:, michaelmas 2024 (closed).

Some courses can close early. See the Deadlines page for guidance on when to apply.

Funding Deadlines

These deadlines apply to applications for courses starting in Michaelmas 2024, Lent 2025 and Easter 2025.

Similar Courses

• Education (Mathematics Education) PGCE entry only MEd
• Master of Education (Mathematics Education) PACES entry only MEd
• Medical Education PGCert
• Applied Mathematics and Theoretical Physics PhD
• Learning Design and Teaching Innovation PGCert

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Study Postgraduate

Phd in mathematics (2022 entry), explore our phd in mathematics.

The PhD in Mathematics offers an intellectually stimulating and dynamic atmosphere research in both pure and applied mathematics. Study at the University of Warwick's Mathematics Institute, ranked 3rd in the UK in REF 2014, an international centre of research excellence.

Course code

3 October 2022

3 to 4 years full-time

Qualification

Mathematics Institute

University of Warwick

About this research graduate course

Course overview.

Mathematics at Warwick covers a full range of both pure and applied areas. The Mathematics Postgraduate Degrees are appropriate for students with a strong and broad mathematical background who wish to continue to focus on primarily mathematical questions in their postgraduate work.

All students are required to undergo training in Year One and are encouraged to make use of further training opportunities available in subsequent years. Training ranges from gaining a broader knowledge of mathematics through taught modules, seminars and workshops, to enhancing your professional and transferrable skills. Our aim is to produce excellent PhD students who have undertaken high quality original research and who are well-prepared for a career, either in academia or elsewhere.

Teaching and Learning

Students are required to complete a series of modules in theirs first year (from a very wide selection of bespoke modules), with assessment including an oral examination component. Upon the successful completion of these modules, students are required to complete research project before being formally upgraded to a PhD at the end of the first year.

Training will be supplemented with attendance to seminars, cohort building activities, and additional transferable skills training.

General entry requirements

Minimum requirements.

First Class integrated MA, MMath or MSc degree in Mathematics or a science degree with high mathematical content.

English language requirements

You can find out more about our English language requirements . This course requires the following:

• IELTS overall score of 6.5, minimum component scores not below 6.0

International qualifications

We welcome applications from students with other internationally recognised qualifications.

For more information, please visit the international entry requirements page .

Additional requirements

There are no additional entry requirements for this course.

Our research

The mathematics department covers a wide range of research areas in mathematics and its applications.

You may also wish to explore the research interest of current Warwick academics .

Find a supervisor

The 'Find A Supervisor' link below will allow you to explore the research interests of academics within the department. Please include in your application the names of potential supervisors, with interests aligned with yours, or people you would like to work with.

The mathematics department, unlike some other departments, does not require students to make any arrangements with any potential supervisors before applying, though of course you are welcome to contact them directly and discuss your interests and any potential projects they may offer.

Tuition fees

Tuition fees are payable for each year of your course at the start of the academic year, or at the start of your course, if later. Academic fees cover the cost of tuition, examinations and registration and some student amenities.

Taught course fees   Research course fees

Fee Status Guidance

We carry out an initial fee status assessment based on the information you provide in your application. Students will be classified as Home or Overseas fee status. Your fee status determines tuition fees, and what financial support and scholarships may be available. If you receive an offer, your fee status will be clearly stated alongside the tuition fee information.

Do you need your fee classification to be reviewed?

If you believe that your fee status has been classified incorrectly, you can complete a fee status assessment questionnaire. Please follow the instructions in your offer information and provide the documents needed to reassess your status.

Find out more about how universities assess fee status

Additional course costs

As well as tuition fees and living expenses, some courses may require you to cover the cost of field trips or costs associated with travel abroad. Information about department specific costs should be considered in conjunction with the more general costs below, such as:

As well as tuition fees and living expenses, some courses may require you to cover the cost of field trips or costs associated with travel abroad.

For departmental specific costs, please see the Modules tab on the course web page for the list of core and optional core modules with hyperlinks to our  Module Catalogue  (please visit the Department’s website if the Module Catalogue hyperlinks are not provided).

Associated costs can be found on the Study tab for each module listed in the Module Catalogue (please note most of the module content applies to 2022/23 year of study). Information about module department specific costs should be considered in conjunction with the more general costs below:

• Core text books
• Printer credits
• Dissertation binding
• Robe hire for your degree ceremony

Scholarships and bursaries

Scholarships and financial support

Find out about the different funding routes available, including; postgraduate loans, scholarships, fee awards and academic department bursaries.

Mathematics Funding Opportunities

Find out more about the various funding opportunities that are available in our department.

Living costs

Find out more about the cost of living as a postgraduate student at the University of Warwick.

Mathematics at Warwick

Our challenging Mathematics degrees will harness your strong mathematical ability and commitment, enabling you to explore your passion for mathematics.

Find out more about us on our website

Our courses

• Interdisciplinary Mathematics (Diploma plus MSc)
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• Mathematical Sciences (MASt)
• Mathematics (Diploma plus MSc)
• Mathematics (MSc)
• Mathematics of Systems (MSc leading to PhD)
• Mathematics (PhD)
• Mathematics of Systems (PhD)

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Why Warwick

Discover why Warwick is one of the best universities in the UK and renowned globally.

6th in the UK (The Guardian University Guide 2022) Link opens in a new window

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(The Graduate Market in 2022, High Fliers Research Ltd. Link opens in a new window )

About the information on this page

This information is applicable for 2022 entry. Given the interval between the publication of courses and enrolment, some of the information may change. It is important to check our website before you apply. Please read our terms and conditions to find out more.

PhD Studentship: Advancing Joint Modelling Methodology for Clinical Prediction Models

The university of manchester - mathematics.

This 3.5 year PhD project is funded by the MADSIM Project, https://www.madsim.manchester.ac.uk/ . Funding is for Home students and EU students with settled status. Funding covers home tuition fees and provides a stipend at the UKRI rate (£19,237 for 2024/25). The start date is 1 st October 2024.

This is an interdisciplinary project between the Department of Mathematics (Christiana Charalambous, Timothy Waite) and the Centre for Health Informatics (David Jenkins). Clinical prediction models (CPMs) are algorithms that use information about a patient at a given time point to generate risk estimates for an outcome. These models are widely adopted throughout healthcare and can be used to inform clinical decisions, for example, if an individual should receive an intervention. Traditionally, CPMs have used data from a single time point and often consider a single outcome. However, the adoption of electronic health records and the increase in availability of data provides rich longitudinal (e.g. repeatedly measured biomarkers) and time-to-event (e.g. death or disease progression) data, which are often underutilised. Complex models that use multi-outcome (potentially correlated) data, such as joint models, are increasingly being adopted and evidence from the literature suggests this could improve predictive accuracy and in turn patient outcomes. Nonetheless, there are strong assumptions required and a lack of methodological development for healthcare usage. In addition, it is unclear when repeated longitudinal measurements should be recorded. Objectives and outcomes of the project:

• Review the existing literature on joint modelling for clinical prediction.
• Undertake methodological development for the formulation and validation of joint models, testing the developed methods throughout a range of scenarios in simulated and real-world health data.
• Extend time-dependent AUC methodology for joint model validation.
• Perform simulation studies to compare the proposed method to existing approaches for prediction and model validation.
• Extend current minimum sample size methodology for joint models.
• Undertake simulation studies to investigate the impact of longitudinal measurement frequency on joint model performance.
• Investigate techniques for Bayesian design of experiments in joint models.

The combination of simulation and real-world data will allow us to evaluate the methods under a range of scenarios and parameter combinations and assess the real-world impact of the methods. The collaboration with the Centre for Health Informatics will provide access to real-world health data, such as the Greater Manchester care record, UK Biobank and cardiovascular data from the Manchester University NHS Foundation Trust and Wythenshawe Hospital, that the centre regularly utilises. The project will also provide recommendations to determining when to monitor patients and guidance for developing and validating joint models for clinical prediction.

Applicant’s should have:

• Obtained or working towards a 1st class degree in Mathematics (BSc/MMath) or Distinction level Masters in (Bio)Statistics, Data Science or similar.
• Research experience, e.g. UG/MSc project, research internship or other.
• Background in some or all of the following: longitudinal data analysis, survival analysis, design of experiments, Bayesian statistics.
• Good programming skills in a language such as R or Python
• Good communication skills (oral and written)
• Openness to working across disciplines

Before you apply, please contact Dr Christiana Charalambous at [email protected] .

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